I can recommend a surefire way of getting a student never to forget not to say /kaʊnt/ as the first syllable of that word which is to say that you can't say the correct syllable for them because it would be too improper to utter in polite society since it constitutes currently the single most obscene word in the English language.

You can help him with some kind of explanation (whether adhoc or not), or some mnemonic. In words with 'countV-' , the is historically long. In 'country', is short. In the history of English, you can see many examples where vowels got lightened before clusters.

There is a great book that deals with these kind of phenomena. Check Charles-James Bailey and Karl Maroldt's "Grundzuge der Englischen phonetelogie Allgemeine systametik". The above set of examples came from page 102 of that book. Check Charles-James Bailey's "English Phonetic Transcription" as well.